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Aleks04 [339]
3 years ago
8

Use long division to find a repeated decimal equivalency for the fraction. Upload all of your work as part of your final answer.

The fraction is:
8/9
Mathematics
2 answers:
s344n2d4d5 [400]3 years ago
6 0
Its simple just divide
Kay [80]3 years ago
3 0
You would divide 8 by 9, because the is inside the bracket division sign.
Hope this helps!
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Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
2 years ago
11) Wayne exercised for 5/6 of an hour in the morning and 1/3 of an hour in the evening. How much more of an hour did Wayne spen
Brums [2.3K]
He spent 3/6 hours more or 30 minutes more
8 0
3 years ago
Emily is entering a bicycle race for charity. Her mother pledges $0.90 for every 0.25 mile she bikes. If Emily bikes 7 miles, ho
mestny [16]

Answer:

Find how much she will be paid per mile to make it easier.

.25 * 4 = 1

.90 * 4 = 3.60

Now you know she earns 3.60 per mile, multiply that by 7.

3.60 * 7 = $25.20 total.


6 0
3 years ago
Read 2 more answers
10.Mr. Vickers earns a 7.5% commission on his total sales. Last month, he had sales of
Leno4ka [110]

Answer:

4096.50, 4,096.50, $4,096.50, or $4096.5

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Write the number 270 as a sum of three numbers so that the sum of the products taken two at a time is a maximum. (Enter the thre
iren [92.7K]

Answer:

x=y=z=90.

Step-by-step explanation:

let the 3 numbers be x,y,z.

let s be sum

s=x+y+z

we need to maximize xy+yz+zx

or , xy + y(270-(x+y))+x(270-(x+y)) = P(x)

Use Lagrange's Multipliers

⇒ΔP= λΔS

⇒\frac{x+y}{x+z} =1

⇒y=x

⇒\frac{x+z}{x+y} =1

⇒z=y

⇒x=y=z

⇒3x = 270

⇒x= 90

hence, x=y=z=90.

3 0
3 years ago
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